We visited the Academy before heading off to the Shangri La tour (Doris Duke's estate - tickets booked through the Academy). The Academy is worth a few hours of one's time. They have all sorts of collections, from European and Middle Eastern to Chinese and Japanese.
They also have a lovely collection of Hawaiian and Polynesian art. We
principally focused on those and on a wonderful exhibit about a local architect. The building itself is lovely, with beautiful courtyards in
which to relax. The Academy also has an excellent cafe', which is very
popular and to which you will likely need reservations (I suppose that
if we had made them before starting to look around, we would have gotten a seat). In any event, no reservations are not a problem because anything on the menu can be prepared for take out and eaten in
one of the courtyards of the museum. Try the Asian courtyard with its gurgling koi pond and very exotic feel. A wonderful escape. The Academy is easily reachable by bus.